A very unfortunate brief before us;
1. I suggest (your sister’s) husband to file Divorce suit matter under "cruelty and un-curable unsound mind" grounds using S. 13 (1) (iii) HMA (assuming parties marriage falls under Hindu marriage laws) and present his evidences and well drafted pleading paras right from wife's treatment to her various Dr.'s evidences and all medical records and let they all be cross examined including himself and FIL (wife's father). Pleadings as well as witness cross examination should point to un-curability of her unsound mind resulting into cruelty to husband remember it.
2. Since a disabled minor son of parties is currently with her husband based on well plead r/w evidences and cross examination he will retain custody of minor and she may apply under S. 26 HMA for child visitation.
3. The Hon'ble Court if satisfied by her husband's side's pleadings, evidences, witness statements and cross -examination of parties followed by final arguments then may grant divorce to parties but may also grant alimony to wife as well as under S. 27 HMA grant return of her stridhan (jewelry which you say is with them is what I mean here) too.
It seems lady’s family has come in terms to get divorce for the lady thus asking if her father can represent her?. Unfortunately only under ‘insanity or if she is a minor’ clause any other person known to her could have been allowed to represent her, but, she being major and mother of a minor child along with probably un-curable unsound mind she cannot be represented by her father initially when the case is admitted.
Hence tell her husband to hire a seasoned advocate locally who is found via reference and ask her husband to file divorce on above suggested ground (para 1).
To your question on your father filing divorce on behalf of your sister, I am sorry to say there is no such provision based on your presented brief for reason mentioned in above para. However your father can represent her under marked and exhibited PoA which may be questionable appeal ground in High Court if any hence safe way to litigate in this brief is mentioned under above paras.
Also note her husband has to prove beyond reasonable doubt your sister’s “un-curable unsound mind” to get a divorce decree and this is very / highly subjective ground totally based on her medical doctors opinion under Oath r/w cross examination her “un-curable unsound mind” and if any (other) witnesses statements r/w cross examinations based, as highest degree of proof is attributed under Hindu Law to prove this ground.